1. **State the problem:** We have a right triangle with a 60° angle, hypotenuse 9, and legs labeled $x$ and $y$. We need to find the missing side lengths $x$ and $y$. 2. **Recall the properties of a 30°-60°-90° triangle:** In such a triangle, the sides are in the ratio $1 : \sqrt{3} : 2$, where the hypotenuse is twice the shortest leg. 3. **Identify the sides:** Since the hypotenuse is 9, the shortest leg (opposite 30°) is half of 9, so: $$x = \frac{9}{2} = 4.5$$ 4. **Find the other leg (opposite 60°):** It is $\sqrt{3}$ times the shortest leg: $$y = 4.5 \times \sqrt{3} = \frac{9}{2} \times \sqrt{3}$$ 5. **Simplify $y$:** $$y = \frac{9\sqrt{3}}{2} \approx 7.79$$ **Final answers:** $$x = 4.5$$ $$y = \frac{9\sqrt{3}}{2} \approx 7.79$$